Let the two required numbers be x and y, then x - y = 176, thus y = x - 176.
Let the product of the two numbers be represented by
[tex]P = xy x(x - 176) = x^2 - 176x[/tex]
For the product to be minimum, [tex] \frac{dP}{dx} =0[/tex]
[tex] \frac{dP}{dx} =2x - 176=0 \\ \\ \Rightarrow2x=176 \\ \\ \Rightarrow x=88[/tex]
Thus, y = 88 - 176 = -88
Therefore, the two numbers are 88 and -88.
